Fig. 7: Spontaneous waves reflect structured fluctuations in E/I balance that sparsely modulate spike probability.

a Membrane voltage for a simulated neuron in either the sparse-wave network (black line) or dense-wave network (purple line) calculated from the summed excitatory and inhibitory synaptic currents received by that neuron. Spiking activity occurred when the voltage crosses the threshold (V_th red line). The distribution of membrane potentials over the interval for the sparse and dense networks is plotted on the right. b The amplitude of the simulated LFP (blue line) and the relative level of excitatory and inhibitory conductance (red line) over a 10 × 10 neuron pool were counter phase. c Scatter plot of LFP and g_e − g_i difference revealed a significant negative correlation (N = 50,000 time points; Pearson’s r = −0.83; CI test, α = 0.01). d Spike-phase coupling was significant across networks in the asynchronous-irregular regime, and the degree of coupling was correlated with the magnitude of synaptic conductance (N = 599 simulations; Pearson’s r = 0.78 ± 0.001, 95% CI). e Histogram showing the fraction of spikes that occurred during each phase of the simulated LFP in the topographically connected network. Spike probability was modulated by the LFP phase (N = 22 resamples vs. shuffle; spike-phase index = 0.15). f Same as in (e), but for recorded cortical data. Spike probability was similarly modulated (spike-phase index = 0.16; N = 22 recording sessions vs. shuffle). g The dense-wave network simulation had a significantly stronger spike-phase relationship (N = 10 resamples; spike-phase index = 0.44, p = 0.0000085, two-tailed Wilcoxon’s rank-sum test).